## Linear Operators: Spectral operators |

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Page 2143

Then, in the conjugate space X*, there is a unique

spectral measure on the a-field M(T) of sets measurable T which is countably

additive on J((T) in the X topology of X*. This unique

Then, in the conjugate space X*, there is a unique

**extension**of the**adjoint**E* to aspectral measure on the a-field M(T) of sets measurable T which is countably

additive on J((T) in the X topology of X*. This unique

**extension**is bounded and ...Page 2530

On the existence of J -self

adjoint. Coram. Pure Appl. Math. 15, 423-425, (1962). Gamelin, T. W. (see also

Balslev, E.) 1. Decomposition theorems for Fredholm operators. Pacific J. Math.

On the existence of J -self

**adjoint extensions**of J -symmetric operators withadjoint. Coram. Pure Appl. Math. 15, 423-425, (1962). Gamelin, T. W. (see also

Balslev, E.) 1. Decomposition theorems for Fredholm operators. Pacific J. Math.

Page 2551

The spectra of minimal self-

Math. 12, 1003-1022 (1962). 2. Spectral measures, generalized resolvents, and

functions of positive type. J. Math. Anal. Appl. 11, 447-477 (1965). Maokey, G. W.

...

The spectra of minimal self-

**adjoint extensions**of a symmetric operator. Pacific J.Math. 12, 1003-1022 (1962). 2. Spectral measures, generalized resolvents, and

functions of positive type. J. Math. Anal. Appl. 11, 447-477 (1965). Maokey, G. W.

...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator algebra of projections Amer analytic arbitrary asymptotic B-space Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator bounded spectral commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote differential operator disjoint Doklady Akad domain eigenvalues elements equation equivalent exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial preceding Proof properties prove quasi-nilpotent restriction Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset Suppose trace class type spectral operator unbounded uniformly bounded unique vector weakly complete zero